Writing, rather than phoning, is probably the best way to contact aliens, U.S. scientists say.

So instead of phoning home, it could have been more energy efficient if ET had inscribed information and physically sent it, because radiowaves disperse as they travel.

"Think of a flashlight beam," said Professor Christopher Rose, of Rutgers University in New Jersey, who reported his finding in today's issue of the journal Nature.

"Its intensity decreases as it gets farther from its source. The same is true of the beam of a laser pointer, though the distance is much longer," he added.

"If haste is unimportant, sending messages inscribed in some material can be strikingly more efficient than communicating by electronic waves."

Scientists have known that radiowaves can, in principle, be used to communicate over interstellar distances.

And Rose and his colleague, physicist Dr Gregory Wright, were pondering how to get the most bits per second over a wireless channel.

They concluded that the detectability of a signal diminished with distance. Essentially the radiowaves were 'diluted' as they travelled through space, meaning much of their energy was wasted, even if some of the signal reached the target.

That 'dilution' could also cause a problem for aliens trying to contact Earth.

The researchers argued that for a civilisation to send anything other than a basic message over a large distance using radiowaves, it would have to build a huge antenna, the size of the Earth.

If the recipient wasn't listening or missed it, the message may have to be sent many times.

Message in a bottle

The suggestion that written information may be a better way of communicating with aliens is not new. But the U.S. researchers were the first to provide quantitative evidence for, essentially, leaving a 'message in a bottle'.

A physical message encoded in an object could have benefits for both the sender and the receiver as it lands somewhere and stays there, the researchers said.

Messages from aliens could possibly be embedded in organic material in an asteroid, for example. They could also be in the crater made as it hits the Earth.

Professor Woodruff Sullivan, from the University of Washington in Seattle, said sending signals was the best way to communicate with extraterrestrials over short distances.

"But perhaps some attention should be paid to the possibility of one day finding in our solar system an information-drenched artefact, sent by an extremely advanced extraterrestrial civilisation interested only in one-way communication," he said.

He said the people who sent this could be "orbiting the sun or a planet, or resting somewhere on a planet, moon or asteroid".

"The scenario is reminiscent of Arthur C Clarke's 2001: A Space Odyssey, in which a monolith discovered on the Moon has been left by extraterrestrials."